Constraining the shape of a gravity anomalous body using reversible jump Markov chain Monte Carlo

TL;DR

This paper introduces a Bayesian RJMCMC method to effectively constrain the shape of gravity anomalous bodies in trans-dimensional geophysical inversion, providing solutions with quantifiable uncertainty.

Contribution

It develops a novel RJMCMC algorithm with specialized moves to improve efficiency in trans-dimensional gravity inversion problems.

Findings

The algorithm successfully estimates the shape and size of underground bodies.

It produces parsimonious models with fewer parameters among high-probability solutions.

Numerical experiments validate the method's effectiveness in 2-D cases.

Abstract

Typical geophysical inversion problems are ill-posed, non-linear and non-unique. Sometimes the problem is trans-dimensional, where the number of unknown parameters is one of the unknowns, which makes the inverse problem even more challenging. Detecting the shape of a geophysical object underneath the earth surface from gravity anomaly is one of such complex problems, where the number of geometrical parameters is one of the unknowns. To deal with the difficulties of non-uniqueness, ill-conditioning and nonlinearity, a statistical Bayesian model inference approach is adopted. A reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is proposed to overcome the difficulty of trans-dimensionality. Carefully designed within-model and between-model Markov chain moves are implemented to reduce the rate of generating inadmissible geometries, thus achieving good overall efficiency in the Monte Carlo sampler. Numerical experiments on a 2-D problem show that the proposed algorithm is capable of obtaining satisfactory solutions with quantifiable uncertainty to a challenging trans-dimensional geophysical inverse problem. Solutions from RJMCMC appear to be parsimonious for the given prior, in the sense that among the models satisfactorily represent the true model, models with higher posterior probabilities tend to have fewer number of parameters. The proposed numerical algorithm can be readily adapted to other similar trans-dimensional geophysical inverse applications. Keywords: trans-dimensional geophysical inversion, reversible jump Markov chain Monte Carlo; gravity anomaly.